Inter-transaction times and long memory of financial time series

Tomasz Gubiec, Jarosław Klamut, Ryszard Kutner

There are many well known and universal properties of the financial time series called stylized fact. One of them states that autocorrelation of increments of the financial time series decays very quickly while the one of their absolute values decays very slowly. The latter property is strongly related to the phenomena of volatility clustering. By using high frequency empirical data we state that The foundation of this type of behavior is indeed the long-term autocorrelation of inter-event times. Such dependence can be described in terms of the stochastic model based on Continuous-Time Random Walk [1], the model introduced by physicists Montroll and Weiss nearly 50 years ago [2]. The model with dependent inter-event times can significantly contribute to successful description of high-frequency financial data by CTRW [3,4].